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Symmetry 2014, 6(2), 396-408; doi:10.3390/sym6020396
Article

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

*  and
Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
* Author to whom correspondence should be addressed.
Received: 24 February 2014 / Revised: 12 May 2014 / Accepted: 14 May 2014 / Published: 22 May 2014
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
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Abstract

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.
Keywords: ΡT symmetry; SL(2, C); Lorentz group; Hyperbolic geometry ΡT symmetry; SL(2, C); Lorentz group; Hyperbolic geometry
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Sánchez-Soto, L.L.; Monzón, J.J. Invisibility and PT Symmetry: A Simple Geometrical Viewpoint. Symmetry 2014, 6, 396-408.

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